The challenges will be even greater when House and Senate bills have to be combined. Among the differences that need to be resolved are whether to include the option of a government-run insurance plan to compete with the private sector, how to pay for overhaul costs and where to levy taxes.

Democrats also have to be careful about losing Snowe's support. Even though she voted aye for the Baucus bill, Snowe said her vote doesn't forecast what her vote will be in the future.

Sen. Jay Rockefeller, D-W.Va., who had expressed reservations about the Baucus bill, said during the committee hearing Tuesday, "We are not doing what we set out to do. It is a step in the right direction, but it is not enough."

Public option is likely to be one of the thorniest issues in the debate moving forward. Snowe today expressed concern about including that option, saying she would prefer to first give the private insurance industry a chance to oblige with new requirements set for them.

"I would prefer to allow the private sector to work through these reforms that we are going to require of them," Snowe said. "They're going to have to live up to a certain standard. If they don't, then you can have a public option kick in immediately."

Snowe was the one of the first to suggest the idea of a trigger public option, whereby a government plan would be implemented in regions where private insurance companies did not offer affordable, accessible coverage.

House Democrats are particularly sensitive about the public-option issue. Many of them don't support Baucus' bill because it doesn't include that plan. Instead, Baucus proposed the creation of member-owner, nonprofit co-operatives that would compete with private insurers.

"There is no doubt about it, through this process the Senate bill has gotten watered down and watered down and watered down," Rep. Anthony Weiner, D-N.Y., told ABC News.

Feuding Democrats say the president needs to step in and offer a compromise.

"This is kind of like a baseball game where you bring in your best pitcher at the end to be your closer," Weiner said. "Well, those of us who support a public option are waiting for President Obama to come in out of the bull pen and seal this deal. Up to now every committee has moved this ball forward, now have to make sure we get it right. One thing is clear, if we don't have true competition and true cost containment that only public option can create, we're going to regret this effort in the end."